Physics:Damping matrix

In applied mathematics, a damping matrix is a matrix corresponding to any of certain systems of linear ordinary differential equations. A damping matrix is defined as follows. If the system has n degrees of freedom u_n and is under application of m damping forces. Each force can be expressed as follows:

$f_{Di}=c_{i1}\dot{u_1}+c_{i2}\dot{u_2}+\cdots +c_{in}\dot{u_n}=\sum _{j=1}^n{c}_{i,j}\dot{u_j}$

It yields in matrix form;

$F_D=C\dot{U}$

where C is the damping matrix composed by the damping coefficients:

$C=(c_{i,j}{)}_{1\le i\le n,1\le j\le m}$

References

• (fr) Mechanics of structures and seisms